The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the models it makes. Suppose that the mpgʹs for the five models of a manufacturer are 19, 21, 22, 28, and 18, and the government requirement is 25 mpg. The last of the models is to be redesigned to meet the government requirement. What must the new mpg of this model be to meet the requirement?

Question

Mathematics

Richard

26 July, 17:35

The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the models it makes. Suppose that the mpgʹs for the five models of a manufacturer are 19, 21, 22, 28, and 18, and the government requirement is 25 mpg. The last of the models is to be redesigned to meet the government requirement. What must the new mpg of this model be to meet the requirement?

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Brooklynn Osborn · Answer 1

25 mpg

Step-by-step explanation:

We have a set of values 19, 21, 22, 28 and 18

The average (which is the mean of the set of values) is:

19 + 21 + 22 + 28 + 18 = 21.6 mpg out of the government requirement

So we need a value such as the mean become at least 25 mpg

We have to solve the equation:

(19+21+22+28 + x) / 5 = 25

(90 + x) / 5 = 25 ⇒ 90 + x = 125 ⇒ x = 35 mpg

If we get the mean of the set of values including 35 we have:

(19 + 21 + 22 + 28 + 35) / 5 = 25 mpg government requirement